Theoretrical derivation of mutual coupling and radiation properties of loop antenna arrays valid from rf to optical

Circular loop antenna arrays are extremely useful for a wide variety of applications, including geophysical sensing and communications. In the optical regime, these structures are especially useful for solar energy harvesting. One of the most difficult to achieve enabling technologies for these applications is superdirectivity. Rapid design and analysis of these devices requires accurate and efficient calculations for the mutual coupling and radiation properties. Due to the complexity of the integrals involved in the calculations, numerical full-wave solvers are often employed. Unfortunately, these are often time-consuming and memory-intensive. Closed-form analytical solutions would allow the designer to rapidly analyze the radiation characteristics of an array and lead to extremely efficient optimizations. This paper presents straightforward analytical expressions for computing the radiation properties of arrays including the effects of mutual coupling. The theory is general enough to take into account dispersion and loss of materials at optical frequencies. It will be shown that full-wave simulations for a simple 2×1 array of nanoloops can take up to six hours, while the analytical implementations take less than a minute. As an illustrative example, a broadband highly directive array will be optimized and the resulting design will be validated with full-wave simulations.